Limit of root expressions using the x^n - a^n form

This type of question, asked 4 times: 19 Apr 2025 S1, 19 Apr 2025 S2, 13 Apr 2026 S1, 15 Apr 2026 S2. All 4 questions below, oldest first.

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Question 1
19 Apr 2025 S1
108 $\underset{x\rightarrow 3}{\lim} \frac{(84 -x)^{\frac{1}{4}}- 3}{x- 3}$
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Question 2
19 Apr 2025 S2
132 $f(x) =\frac{(27 - 2x)^{\frac{1}{3}}- 3}{9 - 3(243 + 5x)^{\frac{1}{5}}},x\neq 0$
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Question 3
13 Apr 2026 S1
71 $f(x) = \begin{cases} \dfrac{(8 - 2x)^{\frac{1}{3}} - 2}{3 - (243 + 5x)^{\frac{1}{5}}}, & \text{if } x \neq 0 \\ k, & \text{if } x = 0 \end{cases}$
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Question 4
15 Apr 2026 S2
71 $f(x) = \dfrac{(256 - 8x)^{\frac{1}{4}} - 4}{16 - 4(64 + 3x)^{\frac{1}{3}}}, x \neq 0$
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Question 1